Discrete Fourier Transform of Windowing Functions

This Demonstration illustrates the frequency domain properties of various windows, which are very useful in signal processing.
All the windows presented here are even sequences (symmetric about the origin) with an odd number of points. An -point discrete Fourier transform (DFT) is of length , where is a positive integer. If the length of the input sequence is less than , then it is padded with trailing zeros to length and the DFT is computed. Here, the length of the input sequence is always taken to be less than the length of the DFT.


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F. J. Harris, "On the Use of Windows for Harmonic Analysis with Discrete Fourier Transform," Proceedings of the IEEE, 66(1), 1978 pp. 51–83.
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